Klebsiella pneumoniae phages vB_KpnP_SU503 (SU503) and vB_KpnP_SU552A (SU552A) are virulent viruses belonging to the Autographivirinae subfamily of Podoviridae that infect and kill multi-resistant K. pneumoniae isolates. Phages SU503 and SU552A show high pairwise nucleotide identity to Klebsiella phages KP34 (NC_013649), F19 (NC_023567) and NTUH-K2044-K1-1 (NC_025418). Bioinformatic analysis of these phage genomes show high conservation of gene arrangement and gene content, conserved catalytically active residues of their RNA polymerase, a common and specific lysis cassette, and form a joint cluster in phylogenetic analysis of their conserved genes. Also, we have performed biological characterization of the burst size, latent period, host specificity (together with KP34 and NTUH-K2044-K1-1), morphology, and structural genes as well as sensitivity testing to various conditions. Based on the analyses of these phages, the creation of a new phage genus is suggested within the Autographivirinae, called "Kp34likevirus" after their type phage, KP34. This genus should encompass the recently genome sequenced Klebsiella phages KP34, SU503, SU552A, F19 and NTUH-K2044-K1-1.